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Math Help - Constraints Word Problem??

  1. #1
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    Constraints Word Problem??

    I need help with this problem that I'm not sure about:

    A company manufacturers two types of boat lifts. Each size requires some time in the welding and assembly department and some time in the parts and packaging department. The smaller lift requires 3/4 hour in welding and assembly and 1 and 2/3 hours in parts and packaging. The larger lift requires 1 and 1/2 hours in welding and assembly and 1 hour in parts and packaging. The factory has 156 hours/day available in welding and assembly, and 174 hours in parts and packaging. Furthermore, daily demand for the lifts is at most 200 large lifts and at most 250 small lifts and the profits are $50 for each large lift and $30 for each small lift.

    1. How many of each type of lift should be manufactured each day to maximize profit? What is maximum profit?

    2. Obtaining additional quantities of which contraint items would have the potential to increase the company's profit? Explain?


    I would really appreciate the answer as well as an explanation for the two questions. This will help me immensely on an exam. Thank you.
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  2. #2
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    Quote Originally Posted by westside7 View Post
    I need help with this problem that I'm not sure about:

    A company manufacturers two types of boat lifts. Each size requires some time in the welding and assembly department and some time in the parts and packaging department. The smaller lift requires 3/4 hour in welding and assembly and 1 and 2/3 hours in parts and packaging. The larger lift requires 1 and 1/2 hours in welding and assembly and 1 hour in parts and packaging. The factory has 156 hours/day available in welding and assembly, and 174 hours in parts and packaging. Furthermore, daily demand for the lifts is at most 200 large lifts and at most 250 small lifts and the profits are $50 for each large lift and $30 for each small lift.

    1. How many of each type of lift should be manufactured each day to maximize profit? What is maximum profit?

    2. Obtaining additional quantities of which contraint items would have the potential to increase the company's profit? Explain?


    I would really appreciate the answer as well as an explanation for the two questions. This will help me immensely on an exam. Thank you.
    Hi westside7,

    This is a linear programming model.

    Let L1 = # of small lifts to be manufactured.

    Let L2 = # of large lifts to be manufactured.

    Constraint 1: L1 <= 250

    Constraint 2: L2 <= 200

    Constraint 3: .75 L1 + 1.5 L2 <= 156

    Constraint 4: 5/3 L1 + 1 L2 <= 174

    The profit function is P(L1, L2) = 30 L1 + 50 L2
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